Generalized Design Approach for Fourth-Order Difference Co-Array

This paper presents a generalized approach to design fourth-order non-uniform linear arrays (NLAs) by combining any two second-order NLAs (e.g. co-prime array (CA), nested array (NA)). This new-formed NLA could exactly achieve a large hole-free range in its fourth-order difference co-array. By establishing the relationship between the second-order NLAs and the fourth-order NLAs, closed-form expressions for the physical sensor locations and the corresponding virtual sensor configurations are specifically derived. Compared to the prior proposed structure, the new structure could effectively increase the virtual aperture, therefore, having the ability to detect more sources. By considering direction of arrival (DOA) estimation for quasi-stationary (QS) signals, numerical simulation results validate the effectiveness of the proposed array structure.